where \(c>0\)  is a constant, it follows that conditions (REF ), (REF ) and (REF ) are satisfied. In particular, Theorem REF  may be applied whenever \(c>0\)  is small enough. On the other hand, it is easy to see that the sequence \(\mathbb {A}=(A_n)_{n\in \mathbb {N}}\)  does not admit a nonuniform strong exponential dichotomy. Therefore, previously known results such as the one in [1]} can not be applied to this example.

